Foundations Of Dynamics

Near the beginning of the Principia Newton interrupted his presentation of the mathematical theory to discuss at some length the basic concepts of his new dynamics. He was writing a pioneering treatise on "natural philosophy," something that was still not quite mathematical physics in the modern sense, and it was not surprising to find such explanatory remarks about the foundations of the subject. Newton's intent was to provide compelling evidence for the absolute character of space and time.

A fundamental law of Newton's mechanics asserts the proportionality of the force acting on a body to its acceleration. If a body is moving with constant velocity, then its acceleration is zero, and the total force acting on it is zero. This fact is related to something called the restricted principle of relativity, also called the Galilean principle of relativity because a version of it was formulated by Galileo. In studying motion we measure the velocity of a body with respect to some time taken as given and with respect to some object taken at rest. This velocity is the relative velocity of the body measured with respect to the rest object. If we consider a system of bodies interacting in any way and impose a uniform velocity of translation on the whole system, then the acceleration and therefore the force of this motion is zero, and it follows that the interactions of the bodies remain unchanged. For example, on a ship sailing with a steady velocity on the open sea the objects within the ship interact mechanically just as they would if they were situated on land.

Motion measured with respect to a reference object is relative motion. Newton held that there is also such a thing as absolute motion, motion measured with respect to absolute time and absolute space. Given two objects moving with a nonzero velocity relative to each other, it follows that the motion of at least one of the bodies is true and absolute. The existence of absolute motion follows because forces are real, and forces are proportional to acceleration. Because the acceleration of a body is associated with a real tangible force, this acceleration must occur as part of an absolute or true motion and cannot be something that is only measured according to some convention with respect to a group of reference objects.

The principle of the relativity of motion does not hold for acceleration because acceleration brings with it dynamical effects. Newton illustrated this fact using examples of circular motion, where centripetal forces act within the system. Because Jupiter rotates on its axis, it is flattened at the poles; it has the shape of what is known as an oblate spheroid. The rotation gives rise to centripetal forces that vary differentially over the surface of the planet, producing the distortion from a sphere. If one were to assume that Jupiter were at rest and the world system were revolving about it, no forces would act on Jupiter, and it would have the shape of a pure sphere. The accelerative motion of Jupiter is something that is absolute, taking place with respect to absolute time and space and producing real forces acting on the planet. Newton also illustrated this point with the example of two spheres joined by a string, in rotation about their common center of mass. In such a system, there is a force of tension in the string; if all the rest of the matter in the universe were removed, there would still be this force acting. It follows that the circular motion of the spheres is an absolute motion. Accelerations are connected to forces, and forces are real and not conventional. Although accelerative forces indicate the existence of absolute motion, it is nonetheless difficult to determine the precise motion of any given object with respect to absolute space and time. In "System of the World," book three of the Principia, Newton formulated the hypothesis that the center of this system was at rest with respect to absolute space. He took this center to be the center of gravity of the solar system. In effect, Newton identified the whole universe with the solar system, the fixed stars, being uniformly distributed and being very distant, not significantly affecting the position of this center. His belief in an absolute point of rest has been seen as a sign of the influence of residual geocentrism, of an inability to follow some of the implications of his new theory to their logical conclusion.

Newton's views on absolute motion were criticized by his philosophical contemporaries Gottfried Leibniz (1646—1716) and George Berkeley (1685—1753) and have since become the subject of an extensive philosophical literature. In terms of the reception and success of Newtonian mechanics in the eighteenth and nineteenth centuries, these views did not play an important role. In using mechanics to investigate planetary motion, the strength of beams, the vibration of elastic strings, or the behavior of flowing fluids it is unimportant whether one supposes the motion to take place with respect to something called absolute space. Newton seems to have emphasized the absoluteness of space and time partly for psychological reasons. The conception of motion in a universe of absolute time and space was the natural development of the new picture of the world developed by Copernicus and Galileo. An open and potentially infinite universe based mathematically on absolute scales of space and time stood in contrast to the closed relational universe of Aristotle and Ptolemy. The two cosmologies represented two understandings of how God orders the universe: on the one hand, the intimate and literal world depicted in Dante, and on the other, the austere, absolute, and mathematical universe of Newton.

Analysis of such fundamental concepts as space and time would become a subject of interest to physicists in the late nineteenth century, and Newton's conception of absolute motion would be severely criticized, particularly by the physicist Ernst Mach (1838-1916) in his 1883 book The Science of Mechanics; A Critical and Historical Account of Its Development. These criticisms would influence Einstein in his development of the general theory of relativity. In this way the philosophical issues raised by Newton in his discussion of absolute space and time would come to play a role in the evolution of modern theories of the universe.

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